Qubit detection using superconductor devices

This applications claims priority to U.S. Provisional App. No. 63/124,011, filed Dec. 10, 2020, and U.S. Provisional App. No. 63/105,086, filed Oct. 23, 2020, each of which is incorporated by reference herein in its entirety.

This relates generally to superconducting devices, including but not limited to, devices utilizing both superconducting and non-superconducting states.

Superconductors are materials capable of operating in a superconducting state with zero electrical resistance under particular conditions. Superconductors are also capable of operating in a non-superconducting (conducting) state.

Quantum information processing and quantum computing are exciting advances in technology that leverage quantum entanglement and superposition of quantum states to expand the computational capabilities of computer systems. An important aspect of quantum computing applications is the ability to generate and entangle quantum bits (also known as “qubits”), as well as determine a state of the qubit. Current detection methods have poor readout fidelity due high losses in the system between qubit circuitry components and qubit detection (e.g., qubit readout) components. Thus, there is a need for systems and/or devices with more efficient and reliable methods for providing an indication of a state of a qubit. Such systems, devices, and methods optionally complement or replace conventional systems, devices, and methods for determining a state of a qubit.

The present disclosure describes detection circuitry that utilizes superconducting components that can undergo a non-thermal phase transition from a superconducting state to a non-superconducting state. In some circumstances and embodiments, a superconducting component is integrated with or closely coupled to a qubit circuit, thereby reducing losses between the qubit circuit and the qubit state detection circuit, which improves qubit signal amplification and qubit readout reliability and fidelity.

In one aspect, some embodiments, an electrical circuit includes a resonant circuit (e.g., a qubit) and a detection circuit. The resonant circuit has (e.g., generates, produces) a first magnetic flux while the resonant circuit is in a first state and a second magnetic flux while the resonant circuit is in a second state that is different from the first state. The detection circuit includes a superconducting component that is located adjacent to and coupled with the resonant circuit, and an impedance component that is coupled to the superconducting component on one end and configured to be coupled to a second circuit on another end. The superconducting component is configured to receive an input current and to operate in a superconducting state while a temperature of the superconducting component is below a superconducting threshold temperature and a current carried in the superconducting component is below a threshold current of the superconducting component. The superconducting component is also configured to generate a flux-induced current based on a state of the resonant circuit such that the superconducting component carries (i) a first current, less than the threshold current, while the resonant circuit is in the first state and has the first magnetic flux, and (ii) a second current that exceeds the threshold current while the resonant circuit is in the second state and has the second magnetic flux, thereby transitioning the superconducting component to a non-superconducting state while the resonant circuit is in the second state.

In another aspect, some embodiments include a method of operating a detection circuit. The method includes maintaining a temperature of a superconducting component in the detection circuit below a threshold temperature. At least a portion of the superconducting component is coupled to a resonant circuit (e.g., a qubit) such that the superconducting component generates a flux-induced current based on a state of the resonant circuit. An input current (e.g., a bias current) is applied to the detection circuit. In response to the resonant circuit being in a first state, a first flux-induced current is generated in the superconducting component such that a sum of the input current and the first flux-induced current does not exceed a threshold current of the superconducting component and the superconducting component is in a superconducting state. In response to the resonant circuit being in a second state, a second flux-induced current is generated in the superconducting component such that a sum of the input current and the second flux-induced current exceeds the threshold current of the in the superconducting component. The superconducting component transitions from the superconducting state to a non-superconducting state and redirects at least a portion of the input current from the superconducting component to an impedance component of the detection circuit.

In yet another aspect, some embodiments include an electrical circuit that includes a resonant circuit (e.g., a qubit) and a detection circuit. The resonant circuit is configured to generate a first current in a first state and a second current in a second state. The second current is different from the first current and the second state is different from the first state. The detection circuit includes a superconducting circuit and an impedance component that is coupled to the superconducting component on one end and configured, on another end, to be coupled to a second circuit. The superconducting component has a first portion, a second portion distinct from the first portion, a third portion distinct from each of the first and second portions, and a junction joining the first, second, and third portions. The superconducting component has a superconducting threshold temperature and a threshold current density such that operating the superconducting component at a temperature less than threshold temperature and at a current density below the threshold current density is required to operate the superconducting component in a superconducting state. The resonant circuit includes the first portion and third portion of the superconducting component. The first portion of the superconducting component is coupled to receive at least a portion of the first current while the resonant circuit is in the first state and at least a portion of the second current while the resonant circuit is in the second state. The second portion of the superconducting component is configured to receive an input current. The junction is configured to experience current crowding such that a current density at the junction is greater than the threshold current density, and transition to a non-superconducting state in response to a difference between the input current in the second portion and a current in the first portion.

In another aspect, some embodiments include a method of operating a detection circuit. The method includes maintaining a temperature of a superconducting component in the detection circuit below a threshold temperature. The superconducting component includes a first portion, a second portion distinct from the first portion, a third portion distinct from each of the first and second portions, and a junction joining the first, second, and third portions. The superconducting component has a superconducting threshold current density, and operating the superconducting component at a temperature less than threshold temperature and at a current density below the threshold current density is required to operate the superconducting component in a superconducting state. An input current is applied to the second portion of the superconducting component. The resonant circuit includes the first portion and third portion of the superconducting component. The first portion of the superconducting component receives a first current from the resonant circuit while the resonant circuit is in a first state and receives a second current from the resonant circuit while the resonant circuit is in a second state. The second state is different from the first state and the second current is different from the first current. In response to the input current, and the first current or the second current, a current is produced in the superconducting component having a current density at the junction of the superconducting component. In response to the current density at the junction exceeding the threshold current density (e.g., while the resonant circuit is in a second state, or transitions to the second state from the first state), the superconducting component transitions from the superconducting state to a non-superconducting state, and at least a portion of the input current is redirected from the superconducting component to an impedance component of the detection circuit.

Thus, devices and circuits are provided with methods for operating superconducting devices, thereby increasing the effectiveness, efficiency, accuracy, precision, and user satisfaction with such circuits and devices.

Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the various described embodiments. However, it will be apparent to one of ordinary skill in the art that the various described embodiments may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

Many modifications and variations of this disclosure can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. The specific embodiments described herein are offered by way of example only, and the disclosure is to be limited only by the terms of the appended claims, along with the full scope of equivalents to which such claims are entitled.

The present disclosure describes operating superconducting devices to utilize a non-thermal phase transition from a superconducting state to a high-resistance normal state (e.g., rather than a thermal transition to a non-superconducting conductive state). In some embodiments, the superconductor is adapted to transition between the superconducting state and the normal state while the superconducting device carries a current that exceeds a threshold current or a threshold current density of the superconducting device.

is a circuit diagram illustrating a circuitthat includes a resonant circuit(e.g., a qubit circuit) and a detection circuitin accordance with some embodiments. In some embodiments, the resonant circuitis a superconducting qubit (e.g., transmon superconducting qubit) that can have a plurality of states (e.g., energy states). In such cases, the state of the resonant circuitcorresponds to the state of the superconducting qubit. The detection circuitincludes a superconducting componentand an impedance component. The superconducting componentis located (e.g., disposed) adjacent to and coupled (e.g., inductively coupled) with the resonant circuit. The superconducting componenthas a threshold temperature and a threshold current above which the superconducting componenttransitions from a superconducting state to a non-superconducting state. The superconducting componenthas a lower impedance (e.g., zero, or approximately zero impedance) than the impedance componentwhile the superconducting componentis in the superconducting state (e.g., zero impedance in the superconducting state), and a higher impedance than the impedance componentwhile the superconducting componentis in the non-superconducting state. Using the superconducting transition properties (e.g., non-thermal superconducting transition properties) of superconducting componentand the relative impedances of the impedance componentand the superconducting componentin the superconducting and non-superconducting states, the detection circuitis able to redirect the transmission path of electrical current transmitted through the detection circuitsuch that the circuitcan provide a readout (e.g., signal, indication) of the state of the resonant circuit.

In some embodiments, the impedance componentis coupled to a circuit(e.g., a readout circuit) that may include one or more signal amplifiersand/or a data acquisition component. In some embodiments, as shown, the impedance componentis coupled in parallel to the superconducting componentsuch that electrical current transmitted through the detection circuitis transmitted via a path with the least impedance. For example, while the superconducting componentis in the superconducting state, electrical current (e.g., a bias current, an input current) is transmitted through the detection circuitvia the superconducting component, and no current is transmitted through the impedance component; alternatively, the amount of current transmitted through the impedance componentis much less than the amount of current transmitted through the superconducting component(e.g., the amount of current transmitted through the impedance componentis 1% or less, or 5% or less, of the amount of current transmitted through the superconducting component). In contrast, while the superconducting componentis in the non-superconducting state, electrical current is primarily transmitted through the detection circuitvia the impedance component(e.g., in some implementations, the amount of current transmitted through the impedance componentis at least ten (10) times more, at least twenty (20) times more, or at least one hundred (100) times more than the amount of current transmitted through the superconducting component; e.g., in some implementations, superconducting componenthas a resistance greater than 100 kOhm in the normal state, while impedance componenthas a resistance of 1-10 kOhm).

In some embodiments, the impedance componentincludes a resistive component (e.g., a resistor, an electrical component that has a non-zero resistance) that has a higher resistance than the superconducting componentwhile in the superconducting componentis in the superconducting state and a lower resistance than the superconducting componentwhile in the superconducting componentis in the non-superconducting state. In such cases, and when the impedance componentis coupled in parallel to the superconducting component, electrical current is transmitted through the detection circuitprimarily via the superconducting component(e.g., at least 95% or 99% of the current is transmitted via the superconducting component) when the superconducting componentis in the superconducting state, and the electrical current is primarily transmitted via the impedance component(e.g., at least 90% or 95% of the current is transmitted via the impedance component) while the superconducting componentis in the non-superconducting state.

are circuit diagrams illustrating operation of the detection circuit shown inin accordance with some embodiments. In these embodiments, the superconducting componentis maintained at a temperature below the threshold temperature of the superconducting component, and state changes in the superconducting componentdiscussed with respect toare due to currents in portions of the superconducting componentthat change (e.g., increase) so as to exceed, or change (e.g., decrease) so as not to exceed, a current density threshold of the superconducting component.

Referring to, the superconducting componentis configured to receive a bias current (e.g., an input current), denoted inas I. The bias current (I) is below the threshold current of the superconducting componentsuch that the superconducting componentremains in a superconducting state while carrying (e.g., transmitting) the bias current (I) and while the superconducting componentis maintained at a temperature below the threshold temperature of the superconducting component. As shown in, the superconducting componenthas a narrow portion-and a wide portion-. It is noted that because the narrow portion-has a narrower cross-section than the wide portion-, a smaller amount of current is sufficient to transition that portion-to the normal state than the amount of current needed to transition the wide portion-to the normal state.

illustrates operation of superconducting component, of detection circuit, while the resonant circuitis in the first state (e.g., first energy state, first resonant state), resonant circuithas a first magnetic flux corresponding to the first state, and the superconducting componentis maintained at a temperature below the threshold temperature of the superconducting component. In, as in, the superconducting componentis located (e.g., disposed) adjacent to and coupled (e.g., inductively coupled) with the resonant circuit. As a result, the superconducting componentcarries a first flux-induced current that is induced by the first magnetic flux of the resonant circuit. The first magnetic flux is denoted inas Band the first flux-induced current and is denoted inas I. In some embodiments, the first flux-induced current (I) travels (e.g., flows) in the opposite direction as the bias current (I) in the narrow portion-of the superconducting componentsuch that the combination of the bias current and the first flux-induced current (I−I) in the narrow portion-of the superconducting componentis below (e.g., does not exceed) the threshold current of the superconducting componentand/or produces a current density in that portion-of the superconducting componentthat is below (e.g., does not exceed) a threshold current density of the superconducting component. Thus, the portion-of the superconducting componentremains in the superconducting state while simultaneously carrying (e.g., transmitting) the bias current (I) and the first flux-induced current (I).

At the same time, the first flux-induced current a (I) travels (e.g., flows) in the same direction as the bias current (I) in the wide portion-of the superconducting component. However, due to the width (or cross-section) of wide portion, the combination of the bias current and the first flux-induced current (I+I) in the wide portion-of the superconducting componentis below (e.g., does not exceed) the threshold current of the superconducting componentand/or produces a current density in that portion-of the superconducting componentthat is below (e.g., does not exceed) a threshold current density of the superconducting component. Since neither the narrow nor wide portion of the superconducting componenthave currents exceeding a threshold current of the superconducting component, the superconducting componentremains in the superconducting state while the resonant circuit is in the first state.

illustrates operation of superconducting component, of detection circuit, while the resonant circuitis in a second state (e.g., second energy state, second resonant state), different from the first state. It is noted that the resonant circuithas a second magnetic flux, different from the first magnetic flux, while the resonant circuitis in the second state. The superconducting componentis located (e.g., disposed) adjacent to and coupled (e.g., inductively coupled) with the resonant circuitso that the superconducting componentcarries a second flux-induced current that is induced by the second magnetic flux of the resonant circuit. The second magnetic flux (e.g., the magnetic flux associated with the state of the resonant circuit, but at the location of the superconducting component) is denoted inas Band the second flux-induced current and is denoted inas I. In some embodiments, such as when the resonant circuitis a transmon superconducting qubit, the second state may correspond to an excited state (e.g., a qubit excitation state), while a first state of the resonant circuitmay correspond to a non-excited state (e.g., a qubit ground state), or vice versa.

In this example, while the resonant circuitis in the second state, the induced magnetic flux (B) corresponding to the second flux-induced current (I) is directed out of the page, and the second flux-induced current (I) travels (e.g., flows) in a same direction as the bias current (I) in the narrow portion-of the superconducting component, but travels (e.g., flows) in the opposite direction as the bias current in another portion-(e.g., the wide portion-). As a result, in this example, while the resonant circuitis in the second state, the bias and induced current are additive (e.g., travel in the same direction) in the narrow portion-, but subtractive (e.g., travel in opposite directions) in the wide portion-of the superconducting component.

Still referring to, the combination of the bias current and the first flux-induced current (I+I) in the narrow portion-exceeds the threshold current of the superconducting component(e.g., the current density in the narrow portion-exceeds a current density threshold of the superconducting component), and thus, even while the superconducting componentis maintained at a temperature below the threshold temperature, the narrow portion-of the superconducting componenttransitions from the superconducting state to the normal state. At least for a brief instant in time, while the narrow portion-is transitioning to the normal state, the wide portion-may remain in the superconducting state, so long as the current density in the wide portion-does not exceed a current density threshold of the superconducting component.

In, the portions of superconducting componentin the normal state are represented by shaded regions, while the portions of superconducting componentin the superconducting state are unfilled or unshaded (e.g., represented by white space between the lines representing the superconducting component's physical perimeter).

represents the same physical configuration of components as, with the resonant circuitstill in the second state, but at a second time later (e.g., 1 to 20 picoseconds later) than a first time corresponding to. As represented by, the transition of the narrow portion-of the superconducting componentto the normal state (as shown in), causes most (e.g., all, virtually all, at least 99%) of the bias current (I) to flow through the wide portion-of the superconducting component. Stated another way, the increase in resistance of the narrow portion-causes the portion of the bias current that was flowing through the narrow portion-to flow through the wide portion-instead, so long as the wide portion-is in the superconducting state and has zero resistance. In this example, the resulting current (e.g., I−I) in the wide portion-superconducting componenthas a current density that exceeds a current density threshold of the superconducting component, which causes the wide portion-of the superconducting componentto also transition to the normal state. This is sometimes herein called a cascading effect or cascading transition of the superconducting componentto the non-superconducting state. In some embodiments, the entire superconducting componentmay transition to the non-superconducting state in response to the portion-of the superconducting componenttransitioning to the non-superconducting state.

It is noted that while the induced current is represented by the same symbol, I, in both, the magnitude of the induced current may change (e.g., be reduced) when both portions-and-of the superconducting componenttransition to the normal state, due to a large increase in resistance of the superconducting component (e.g., from zero to a resistance greater than 1 kOhm, or greater than 100 kOhm).

In the examples discussed above, the first flux-induced current flows clockwise through the superconducting component, which aligns with the direction of the bias current in the wide portion-and is opposite the direction of the bias current in the narrow portion-of the superconducting component; and the second flux-induced current flows counterclockwise through the superconducting component, which aligns with the direction of the bias current in the narrow portion-and is opposite the direction of the bias current in the wide portion-of the superconducting component. However, even if the bias current were in the opposite direction, and/or the magnetic flux associated with the first and second states of the resonant circuit had the opposite directions from that described above, the superconducting componentwould be in the superconducting state (e.g., having zero or substantially zero resistance) when the resonant circuitis in one state and would be in the normal state (e.g., having a resistance much greater than zero, such as greater than 100 kOhm) when the resonant circuitis in the other state, and thus the resistance of superconducting componentindicates the state of resonant circuit.

Referring to, in response to at least a portion of the superconducting component(e.g., portion-, portions-and-, or the entire superconducting component) transitioning to the non-superconducting state (e.g., when the resonant circuit is in the second state, as described above with reference to), the impedance (and/or resistance) of the superconducting componentis greater than an impedance (and/or resistance) of the impedance componentand thus at least a portion of the bias current (I) is transmitted via the impedance componentinstead of the superconducting component. In some embodiments, such as when the impedance componentis coupled to (e.g., connected to) a circuit(e.g., a readout circuit), the circuitreceives at least a portion of the bias current (I) (e.g., from a current source) and provides an indication (e.g., a signal) that the resonant circuitis in the second state.

In response to the bias current (I) being redirected (e.g., rerouted) through the impedance component, the superconducting componentreceives a smaller portion of the bias current (I) (and in some cases, ceases to receive any portion of the bias current (I)), and the total current carried in the superconducting componentand/or the current density in any portion of the superconducting componentdrops below the threshold current and/or the threshold current density. Thus, the superconducting componenttransitions (e.g., returns) to the superconducting state provided that the superconducting componentis maintained at a temperature below the threshold temperature. The superconducting componentis able to transition back to the superconducting state in the absence of at least a portion of the bias current (I) since the first flux-induced current (I) and the second flux-induced current a (I) are each below the threshold current of the superconducting componentand are not able to, without the addition of at least a portion of the bias current (I), cause any portion of the superconducting componentto have a current density that exceeds the threshold current density. In some embodiments, the bias current is modulated at a frequency, or with a modulation pattern, that prevents superconducting componentfrom transitioning back and forth between the superconducting state and normal state at the same frequency as resonant circuit, and the signal received at circuitis demodulated, e.g., by data acquisition component, to compensate for the modulation of the bias current.

is a schematic diagram illustrating the superconducting componentof the detection circuitshown inin accordance with some embodiments. In some embodiments, as shown, the superconducting componentincludes a loop. In some embodiments, the superconducting componentincludes a superconducting wirethat forms the loop. In some embodiments, the superconducting wire(e.g., a wire made of a superconducting material) has an asymmetrical width such that a first portion of the wire, corresponding to portion-of the superconducting component, has a first width (w), and a second portion of the wire, corresponding to portion-of the superconducting component, has a second width (w) that is greater (e.g., larger) than the first width (w).

In some embodiments, the smaller width (w) in the first portion-of the superconducting component causes current crowding to occur in the first portion-such that for a same electrical current, a current density in the portion-is higher (e.g., greater, larger) than a current density in the second portion-of the superconducting component. Thus, while the superconducting componentcarries a current such that the second portion-of the superconducting componenthas a current density that is below the threshold current density, the current density at the first portion-of the superconducting componentmay exceed the threshold current at the same time that the current density in the second portion-does not exceed the threshold current. While the superconducting componentremains in the superconducting state, the ratio of the current density observed at the first portion-having the first width (w) compared to the current density observed at the second portion-having the second width (w) corresponds to (e.g., is proportional to, or more generally is a function of) the ratio of the second width (w) to the first width (w). Thus, a larger ratio between the second width (w) and the first width (w) results in a more sensitive device, since a smaller amount of current is required for the current density in the portion-of the superconducting componentto exceed the threshold current density of the superconducting componentand for the portion-of the superconducting componentto transition from the superconducting state to the non-superconducting state.

In some embodiments, the portion-of the superconducting componenthaving the first width (w) is located (e.g., disposed) closer to the resonant circuitthan the portion-of the superconducting componenthaving the second width (w). In some embodiments, this is achieved by the first portion-of the superconducting componenthaving the first width (w) being located (e.g., disposed) between the resonant circuitand the portion-of the superconducting componenthaving the second width (w). In some other embodiments, the resonant circuitand the superconducting componentare located on different layers of the circuit, with the portion-of the superconducting componenthaving the first width (w) being located (e.g., disposed) either closer to the resonant circuitthan the portion-of the superconducting componenthaving the second width (w) or at substantially (e.g., within 20%) the same distance from the resonant circuitas the portion-of the superconducting componenthaving the second width (w). In some embodiments, the portion-of the superconducting componenthaving the first width (w) is referred to as a constriction region or a constriction portion.

In some embodiments, a subset, less than all, of the superconducting componentis coupled (e.g., inductively coupled) to the first resonant circuit. For example, the portion-(e.g., the constriction region) of the superconducting componentis coupled to the resonant circuitwhile at least some other portions of the superconducting componentare not coupled to the resonant circuit. In another example, portions of the superconducting componentthat correspond to the loopformed by wireare coupled (e.g., inductively coupled) to the first resonant circuitwhile at least some other portions of the superconducting componentare not coupled to the resonant circuit.

is a circuit diagram illustrating a circuitthat includes a computational circuit(e.g., a quantum computational circuit) that has a plurality of resonant circuits-,-, etc. (e.g., qubit circuits), in accordance with some embodiments. In some embodiments, resonant circuit-may correspond to resonant circuitand thus, the description provided above with respect to resonant circuitinapplies to resonant circuit-. The circuit diagram inis a conceptual representation of the relationship between the different circuits and circuit components in circuit, and is not necessarily a representation of physical relationships between the circuits and circuit components of circuit.

In some embodiments, the computational circuitis a quantum computational circuit that produces, for a given computation, a set of output states (e.g., qubit states). In some embodiments, two or more resonant circuits are coupled to one another such that states (e.g., qubit states) of the coupled resonant circuits are coupled to one another and the coupled resonant circuits exhibit quantum entanglement (e.g., a state of the resonant circuit-is entangled with a state of the resonant circuit-). For example, resonant circuits-and-may be coupled to one another such that when resonant circuit-is in the first state, resonant circuit-is in the second state, and vice versa. In some embodiments, the resonant circuits-and-are coupled to one another via a cavity. Alternatively, the resonant circuits-and-may be capacitively coupled to one another. In another example, the first resonant circuit-and second resonant circuit-are transmon superconducting qubits, and the transmon of the second resonant circuit-is entangled with the transmon of the first resonant circuit-.

Detection circuit(e.g., a detector) is coupled to a respective resonant circuit (e.g., resonant circuit) in the computational circuitand is configured to detect or facilitate detection of a state of the respective resonant circuit in the computational circuit. In some embodiments, circuitincludes a plurality of detector circuits(e.g., detectors) that are each coupled to a corresponding resonant circuitof the computational circuit, and are configured to detect or facilitate detection of a state of the corresponding resonant circuit. In some embodiments, the number of detectorsis equal to the number of resonant circuitsin the computational circuit, while in other embodiments the number of detectorsis less than the number of resonant circuitsin the computational circuit, and thus the detectorsare coupled to a subset, less than all, of the resonant circuitsin the computational circuit.

is a schematic diagram representing an on-chip circuitin accordance with some embodiments. The chip includes a first portionthat is maintained at a temperature below a threshold temperature of superconducting component(e.g., T<T) and a second portionthat can be maintained at a temperature above the threshold temperature of superconducting component(e.g., T>T). For example, in some implementations, the threshold temperature of the superconducting componentis approximately 12 Kelvin (e.g., plus or minus 20%), and the first portionof the chipis maintained at approximately 4 Kelvin (e.g., plus or minus 1 Kelvin) and the second portionof the chipis maintained at temperature of 50 to 300 Kelvin.

The on-chip circuitcorresponds to circuit(shown in) and includes resonant circuitand detection circuit. In some embodiments, as shown in, the resonant circuitand the detection circuit(including the superconducting component) are formed on the same chip (e.g., a same substrate). In some embodiments, the resonant circuitand the detection circuit(including the superconducting component) are located on the first portionof the chipwhile other components of the circuitthat do not include superconducting materials (e.g., voltage source, current source, ground, amplifier(s) (e.g., amplifier(s)), data acquisition component) are located on the second portionof the chip. By placing superconducting components of circuiton the first portionof the chip, the chiponly needs to maintain the first portionbelow a threshold temperature of the superconducting component(s) and the rest of the chipcan be maintained (or allowed to operate) at a higher temperature.

is a side plan view illustrating layering of circuitin accordance with some embodiments. Circuitmay be formed in a stacked configuration where different components of circuitare formed on different layers of a multilayer circuit structure. For example, as shown in inset A and inset B of, components of the detection circuitof circuitare formed on a first layer, and components of the resonant circuitof circuitare formed on a second layerthat is distinct and separate from layer. When circuitis formed in a stacked configuration, as shown, the superconducting componentof the detection circuitoverlaps with at least a portion of the resonant circuitin the z-direction such that the superconducting componentis coupled (e.g., inductively coupled) to the resonant circuit. In some embodiments, by forming the resonant circuitand the detection circuitin separate layers so that the superconducting componentcan overlap with at least a portion of the resonant circuit, the distance between the superconducting componentand the resonant circuitcan be reduced compared to a side-by-side configuration where the between the superconducting componentand the resonant circuitare formed on a same layer. The reduced distance between the superconducting componentand the resonant circuitresults in improved coupling efficiency and thus, can improve the overall accuracy and reliability of circuitin qubit detection.

In some embodiments, a third layeris located (e.g., disposed) between layersandsuch that the components of the detection circuitand the components of the resonant circuitare spaced apart by at least the thickness of layer. For example, layermay be a dielectric layer (e.g., a layer that includes a dielectric material, optionally having a thickness less than 500 nm) that is configured to facilitate coupling (e.g., inductive coupling) between the superconducting componentand the resonant circuit. The thickness and material of layermay improve inductive coupling between the resonant circuitand the superconducting component.

In some embodiments, circuitmay be part of an electronic device and thus, the electronic device may include additional layers, such as layer. In some embodiments, layers of the electronic device, including the layers,, andmay be formed on a same substrate. The different layers may be formed in a different order than shown. For example, the resonant circuitmay be formed on layerand the detection circuitmay be formed on layer. In some embodiments, additional layersmay be located between the substrateand layer.

In addition to improved inductive coupling between the resonant circuitand the detection circuit, forming circuitin a stacked configuration can also provide a compact footprint for circuitand reduce a surface area that needs to be maintained below a threshold temperature of superconducting component(s) (such as superconducting componentand any additional superconducting components in resonant circuit) in the circuit.

illustrate different geometries of a superconducting componentin accordance with some embodiments. Superconducting component-A, shown in, has a same geometry as the superconducting componentshown in. In this embodiment, the superconducting component-A includes a superconducting wirethat forms a loop. In some cases, as shown, the loophas an asymmetrical width such that the superconducting componenthas a first width (w) in a first portion-and a second width (w), that is larger than the first width, in a second portion-. Superconducting component-B has a similar geometry to superconducting component-A except that superconducting component-B includes an indentin the first portion-of the superconducting component. The indentcreates a constriction regionthat further increases the current density in the first portion-of the superconducting componentrelative to other portions of the superconducting component. In some embodiments, except for constriction region, superconducting wireof superconducting component-B has uniform width, or more uniform with than in superconducting component-A.

Referring to, superconducting component-C includes a superconducting wirethat has a cavity, thereby forming superconducting wireas a loop. In some embodiments, the cavityis offset from a center of the superconducting wiresuch that the superconducting wirehas a first width (w) in a first portion-and a second width (w), that is larger than the first width (w), in a second portion-of the superconducting wire. Superconducting component-D has a similar geometry to superconducting component-C except that superconducting component-D includes an indentin the first portion-of the superconducting wire. The indentcreates a constriction regionthat further increases the current density in the first portion-of the superconducting wirerelative to other portions of the superconducting wire. In some embodiments, the cavityof superconducting wireof superconducting component-C is positioned at (or substantially at) the center of the superconducting wire, but indentstill creates a constriction regionthat increases the current density in the first portion-of the superconducting wirerelative to other portions of the superconducting wire.

is a circuit diagram illustrating a circuitthat includes a resonant circuitand a detection circuitin accordance with some embodiments. In some embodiments, the resonant circuitis a superconducting qubit (e.g., transmon superconducting qubit) that can have a plurality of states (e.g., energy states, qubit states). In such cases, the state of the resonant circuitdetermines the state of the superconducting qubit. The detection circuitincludes a superconducting componentand an impedance component. The resonant circuitalso includes at least a portion of the superconducting componentsuch that current carried in the resonant circuitis transmitted through at least a portion of the superconducting componentwhen the superconducting componentis in a superconducting state. The superconducting componenthas a threshold temperature and a threshold current density above which the superconducting componenttransitions from a superconducting state to a non-superconducting state. The superconducting componenthas a lower impedance (e.g., zero, or approximately zero impedance) than the impedance componentwhile the superconducting componentis in the superconducting state (e.g., zero impedance in the superconducting state), and a higher impedance than the impedance componentwhile the superconducting componentis in the non-superconducting state. Using the superconducting transition properties of superconducting componentand the relative impedances of the impedance componentand the superconducting componentin the superconducting and non-superconducting states, the detection circuitis able to redirect the transmission path of electrical current transmitted through the detection circuitsuch that the circuitcan provide a readout (e.g., signal, indication) of the state of the resonant circuit.

In some embodiments, the impedance componentis coupled to a circuit(e.g., a readout circuit) that may include one or more signal amplifiersand/or a data acquisition component. In some embodiments, as shown, the impedance componentis coupled in parallel to the superconducting componentsuch that electrical current transmitted through the detection circuitis transmitted via a path with the least impedance. For example, while the superconducting componentis in the superconducting state, electrical current (e.g., a bias current) is transmitted through the detection circuitvia the superconducting component, and no current is transmitted through the impedance component; alternatively, the amount of current transmitted through the impedance componentis much less than the amount of current transmitted through the superconducting component(e.g., the amount of current transmitted through the impedance componentis 1% or less, or 5% or less, of the amount of current transmitted through the superconducting component). In contrast, while the superconducting componentis in the non-superconducting state, electrical current is primarily transmitted through the detection circuitvia the impedance component(e.g., the amount of current transmitted through the impedance componentis at least ten (10) times more, or at least twenty (20) times more, or at least one hundred (100) times more than the amount of current transmitted through the superconducting component; e.g., in some implementations, superconducting componenthas a resistance greater than 100 kOhm in the normal state, while impedance componenthas a resistance of 1-10 kOhm).

In some embodiments, the impedance componentincludes a resistive component that has a higher resistance than the superconducting componentwhile the superconducting componentis in the superconducting state and a lower resistance than the superconducting componentwhile the superconducting componentis in the non-superconducting state. In such cases, and when the impedance componentis coupled in parallel to the superconducting component, electrical current is transmitted through the detection circuitprimarily via the superconducting component(e.g., at least 95% or 99% of the current is transmitted via the superconducting component) when the superconducting componentis in the superconducting state, and the electrical current is transmitted primarily via the impedance component(e.g., at least 90% or 95% of the current is transmitted via the impedance component) while the superconducting componentis in the non-superconducting state.

are schematic diagrams illustrating a superconducting componentof the detection circuitshown inin accordance with some embodiments. As shown in, superconducting componentincludes a first portion-, a second portion-that is distinct from the first portion-, a third portion-that is distinct from each of the first portion-and the second portion-, and a junction-joining the first, second, and third portions-,-, and-, respectively. In some embodiments, as shown, the superconducting componenthas a Y-shape. In such cases, the first portion-and the second portion-correspond to arms of the Y-shape, the third portion-corresponds a base of the Y-shape, and the junction-corresponds to a middle of the Y-shape that joins (e.g., connects) the arms and base of the Y-shape.

Referring to, the first portion-of the superconducting componenthas a first width (d), the second portion-of the superconducting componenthas a second width (d), and the third portion-has a third width (d). In some embodiments, the second width (d) that is the same as the first width (d). Alternatively, as shown in, the first width (d) of the first portion-may be smaller than the second width (d). In some embodiments, the third width (d) is at least the same or larger than the second width (d). In some embodiments, the third width (d) is at least the same or larger than a sum of the first width (d) and the second width (d).

are circuit diagrams illustrating operation of the detection circuitshown inin accordance with some embodiments. As shown in, the resonant circuitincludes the first portion-and the third portion-of the superconducting component. The first portion-of the superconducting componentis configured to receive current (I) carried in the resonant circuitand transmit the current (I) to the third portion-of the superconducting component. The current (I) is below the threshold current of the superconducting componentand the current density of the current (I) in the first portion-and the third portion-of the superconducting componentis below a threshold current density of the superconducting component. The second portion-of the superconducting componentis configured to receive a bias current (I) (e.g., an input current, such as from a current source) and transmit the bias current (I) to the third portion-of the superconducting component. The bias current (I) is below the threshold current of the superconducting componentand the bias current (I) in the second portion-and the third portion-of the superconducting componentis below a threshold current density of the superconducting component. When the current received at the first portion-and the second portion-of the superconducting component are equal to one another, current crowding effects, such as an accumulation or increase in current density are not observed at the junction-of the superconducting componentand the superconducting componentoperates in the superconducting state (provided that the superconducting componentis maintained at a temperature below the threshold temperature of the superconducting component). In contrast, when the current received at the first portion-and the second portion-of the superconducting component differ from one another in magnitude, current crowding effects are observed at the junction-of the superconducting componentand the current crowding effects can lead to an accumulation or increase in current density at the junction-. The superconducting componentis able to operate in the superconducting state as long as the temperature of the superconducting componentis maintained below the threshold temperature and the current transmitted through the superconducting componenthas a current density that does not exceed the threshold current density of the superconducting component. In the case where the superconducting componentis maintained at a temperature below the threshold temperature and at least a portion of the superconducting componentcarries a current that exceeds the threshold current density of the superconducting component(e.g., via an increase in current density at the junction-due to current crowding effects), the portion(s) of the superconducting componentthat carry a current that has a current density that exceeds the threshold current density of the superconducting componenttransition to the non-superconducting state.